论文标题
带外场的球形自旋玻璃模型
Spherical spin glass model with external field
论文作者
论文摘要
我们分析了2旋球球形Sherrington Kirkpatrick旋转玻璃模型中的自由能和重叠，以了解该模型与没有外部场的模型之间的过渡。我们计算自由能的限制值和波动，以及在外部场的强度随着自旋变量的尺寸增长而变为零的三种类型的重叠。特别是，我们考虑与外场，基态和复制品的重叠。我们的方法涉及分区函数的轮廓积分表示以及随机矩阵技术。我们还为不同缩放制度之间的匹配提供了计算。最后，我们讨论了结果对易感性和吉布斯测量几何形状的含义。本文的一些发现是由兰登（Landon）和索斯（Sosoe）在最近的论文中严格确认的，这些论文同时独立地发表。
We analyze the free energy and the overlaps in the 2-spin spherical Sherrington Kirkpatrick spin glass model with an external field for the purpose of understanding the transition between this model and the one without an external field. We compute the limiting values and fluctuations of the free energy as well as three types of overlaps in the setting where the strength of the external field goes to zero as the dimension of the spin variable grows. In particular, we consider overlaps with the external field, the ground state, and a replica. Our methods involve a contour integral representation of the partition function along with random matrix techniques. We also provide computations for the matching between different scaling regimes. Finally, we discuss the implications of our results for susceptibility and for the geometry of the Gibbs measure. Some of the findings of this paper are confirmed rigorously by Landon and Sosoe in their recent paper which came out independently and simultaneously.
